Transition of Parametrically Driven Cavity Soliton to Soliton Crystals

Temporal cavity solitons (CS) have received significant attention in the past two decades. They stable optical pulses which are governed by the driven damped nonlinear Schrödinger equation [1] and have been experimentally verified in fiber ring cavities [2] and microresonators [3]. In these setups, a coherent pump at frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex> excites the cavity, where CSs emerge on a continuous-wave background through the influence of Kerr (cubic) nonlinearity. Recent work shows that quadratic nonlinearity broadens CS dynamics, enabling optoelectronic phase modulated states [4], [5] and the generation of CSs in synchronously pumped optical parametric oscillators (OPO). In these OPOs, CSs at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex> are parametrically driven by the pump at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\omega$</tex> which replaces the usual pump at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega$</tex>, thus named parametrically driven cavity solitons (PDCS). Their experimental validation includes both fiber ring cavities [6] and microcavities [7]. Systems are classified as singly-resonant, where only the signal resonates [8], or doubly-resonant [9], when both fields resonate.